Place a rack in the center of the oven and preheat to 375°F (190°C).
Pat the chicken breasts dry and season both sides with the kosher salt and black pepper.
Heat 1 tablespoon olive oil in a large ovenproof skillet over medium-high heat. When hot, add the chicken and sear 2–3 minutes per side until golden brown; the chicken does not need to be cooked through. Transfer chicken to a plate.
Reduce heat to medium and add the remaining 1 tablespoon olive oil to the skillet. Add the chopped onion and sauté about 5 minutes until softened.
Add the minced garlic and Italian seasoning to the skillet and stir for 30 seconds, then pour in the pizza sauce and simmer for about 5 minutes.
Return the seared chicken to the skillet, nestling each piece into the sauce. Sprinkle the shredded mozzarella evenly over the chicken and arrange the pepperoni slices on top.
Transfer the skillet to the preheated oven and bake 20–25 minutes, until a thermometer inserted into the thickest part of the chicken reads 165°F (74°C).
Remove from the oven and let rest for a few minutes before serving.